1. What is a 45-45-90 Triangle?

A 45-45-90 triangle is a special right triangle where the two legs are equal in length and the angles opposite them are both 45 degrees. The remaining angle is 90 degrees.

2. How Does the Calculator Work?

The calculator uses the 45-45-90 triangle formula:

Where:

• \( a \) — Length of the equal sides (legs)
• \( h \) — Length of the hypotenuse
• \( \sqrt{2} \) ≈ 1.4142

Explanation: In a 45-45-90 triangle, the hypotenuse is always √2 times the length of each leg.

3. Importance of 45-45-90 Triangles

Details: These triangles are fundamental in geometry and appear frequently in construction, engineering, and design problems. They're especially useful in calculating diagonal distances in square shapes.

4. Using the Calculator

Tips: Enter the length of one side (either leg) in any units. The calculator will compute the hypotenuse length in the same units.

5. Frequently Asked Questions (FAQ)

Q1: What's special about a 45-45-90 triangle?
A: It's an isosceles right triangle where the hypotenuse is always √2 times longer than each leg.

Q2: Can I calculate the legs from the hypotenuse?
A: Yes, the leg length = hypotenuse / √2.

Q3: Where are these triangles commonly found?
A: In squares (diagonal creates two 45-45-90 triangles), in trigonometry problems, and in architectural designs.

Q4: What's the area formula for this triangle?
A: Area = (a²)/2, where a is the length of the equal sides.

Q5: How does this relate to the unit circle?
A: At 45° on the unit circle, x and y coordinates are equal (√2/2, √2/2), forming a 45-45-90 triangle.